Morse-Floer homology is a flourishing algebraic-topological construction in the mathematical toolbox for studying variational problems.
The precursor to Floer homology was first created as a dynamical systems alternative for the intrinsic construction of the homology of compact manifolds — Morse homology [1]}, [2]}, [3]}. Subsequently it has been generalized to many other contexts in analysis and geometry, including infinite dimensional settings.
